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Scientific article
English

Adaptive posterior mode estimation of a sparse sequence for model selection

Contributors

Sardy, Sylvain

Published in

Scandinavian journal of statistics, vol. 36, no. 4, p. 577-601

Publication date

2009

Abstract

For the problem of estimating a sparse sequence of coefficients of a parametric or non-parametric generalized linear model, posterior mode estimation with a Subbotin(λ,ν) prior achieves thresholding and therefore model selection when ν ∈ [0,1] for a class of likelihood functions. The proposed estimator also offers a continuum between the (forward/backward) best subset estimator (ν = 0), its approximate convexification called lasso (ν = 1) and ridge regression (ν = 2). Rather than fixing ν, selecting the two hyperparameters λ and ν adds flexibility for a better fit, provided both are well selected from the data. Considering first the canonical Gaussian model, we generalize the Stein unbiased risk estimate, SURE(λ,ν), to the situation where the thresholding function is not almost differentiable (i.e. ν 1). We then propose a more general selection of λ and ν by deriving an information criterion that can be employed for instance for the lasso or wavelet smoothing. We investigate some asymptotic properties in parametric and non-parametric settings. Simulations and applications to real data show excellent performance.

Keywords

  • Extreme value theory
  • Generalized linear model
  • Gumbel and Fréchet prior
  • Information criterion
  • Lasso
  • ℓν-penalized likelihood
  • Model selection
  • Sparsity
  • Stein unbiased risk estimate
  • Threshold
  • Wavelet smoothing

UNIGE affiliation entities

Citation (ISO format)

SARDY, Sylvain. Adaptive posterior mode estimation of a sparse sequence for model selection. In: Scandinavian journal of statistics, 2009, vol. 36, n° 4, p. 577–601. doi: 10.1111/j.1467-9469.2009.00654.x

Main files (1)

Article (Accepted version)

Identifiers

Journal ISSN

0303-6898
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Technical informations

Creation

01/07/2010 16:15:00

First validation

01/07/2010 16:15:00

Update

14/03/2023 15:49:36

Status update

14/03/2023 15:49:36

Last indexation

29/10/2024 15:42:39
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